Thats kind of a lot to chew on at once, but I'll give it a try.
First, you realize that the 5F6A was pretty much a failure as a bass amp. It became the Holy Grail for may guitarist. Fender was having a hard time limiting the bass response to prevent tearing up the speaker with the huge cone excursions that low frequencies produce. That's why they went to multiple 10" speakers (I've read that in a Fender history book I have some where).
The later Blackface models may be better for your purpose, and frankly, unless you build it yourself there will be compromises. If you want to skip ahead to 6) below, I would not suggest a Bassman as your starting point.
With that in mind:
1) Blackface models already have "Bass Instrument" and "Nornal" channels. The Normal channel is gain > EQ > gain > PI. That's about as 'guitar' as you're going to get if you like Blackface amps.
2) The two inputs are separated as I mentioned, which gives you room to modify them separately too.
3) You will need a separate reverb circuit for reverb, and it would be just like any other Blackface amp where the reverb is on the 'Vibrato' channel. Look at a Twin, Deluxe, etc. schematic for details. Again, unless you build something, you won't get exactly what you want. For off-the-shelf, you could use a reverb pedal on your intended Guitar side.
4) Not that I know of. Really, there is no one amp that does everything well, especially being useful for bass AND guitar.
5) It's not a bad idea to want what you want.
6) It's a good idea to build exactly what you want. Expanding on 3) above, you could have all of this if you look at a Twin, Showman, or Bandmaster head which are already set up for guitar, then modify their respective 'Normal' channels suitable for bass. I suggest a head because you can pick your poison for speakers.